optimization

You want to make a box to contain dirt and your pet earthworm. Using a 7 in by 10 in rectangle of cardboard, you cut congruent squares from the corners and fold up the sides.

Choose the equation would you use in order to do Calculus to find the maximum volume of dirt (including worm) the box can hold?

• $V=\left(7-2x\right)\left(10-2x\right)$

• $V=x\left(7-2x\right)\left(10-2x\right)$

• $V=x\left(7-x\right)\left(10-x\right)$

• $V=x\left(7+2x\right)\left(10+2x\right)$

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

What can you conclude from this number line?

• there is a maximum for A at 12

• there is a minimum for A at 12

• you will have a profitable year

• the stars are aligning nicely

Tags

CCSS.6.NS.C.6

CCSS.6.NS.C.7

Farmer Jo has 32 square feet of land in which to make an enclosure for bunnies, chicks, and penguins. (see picture)

Choose the equation that represents this information.

• $2x+4y=32$

• $2x+2y=32$

• $xy=32$

• $A=3xy$

Tags

CCSS.HSA.CED.A.3

same question, but more ...
There will be fencing put in around the entire enclosure and in the middle (as pictured) to create 3 sections, what dimensions should the overall enclosure be in order to use the least amount of fence?

Which equation represents the fence amount (F) that you want to minimize?

•  $F=2x+4y$ 

•  $F=2x+2y$ 

•  $F=xy$ 

•  $F=3\left(x+y\right)$ 

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

CCSS.HSA.CED.A.3

same question, now solve it and answer the question:

Farmer Jo has 32 square feet of land in which to make an enclosure for bunnies, chicks, and penguins.  There will be fencing put in around the entire enclosure and in the middle (as pictured) to create 3 sections, what dimensions should the overall enclosure be in order to use the least amount of fence?

• The overall enclosure should be 8 feet by 8 feet

• The overall enclosure should be 8 feet by 4 feet

• The overall enclosure should be 32 square feet

• The overall enclosure should be  $\sqrt{128}=8\sqrt{2}$  feet on each dimension

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

CCSS.HSA.CED.A.3

CCSS.HSG.MG.A.3

Pick the correct interpretation from the given number line for V', the derivative of V.

• V has a minimum at 3

• V has a maximum at both 1 and 5

• V has a maximum at 0 and a minimum at 6

• V has a maximum at 1 and a minimum at 5

A square piece of green origami paper that is 6 inches on a side is being made into a gift box (with no lid) by cutting congruent squares out of each corner, folding up the sides, and taping the edges.

What size squares should you cut out for maximum volume? (do the whole problem)

• I should cut out squares that are 1/2 in by 1/2 in

• I should cut out squares that are 1 in by 1 in

• I should cut out squares that are 3 in by 3 in

• I should not cut out any squares

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

A closed rectangular shipping box with square base is to be made from 120 square inches of cardboard. What dimensions should the box be for maximum volume?

Choose the constraint and optimization equations that represent the problem. 

•  $x^2=120$  and  $V=x^3$  

•  $2x+y=120$  and   $V=xy$  

•  $x^2y=120$  and  $V=2x^2+4xy$  

•  $2x^2+4xy=120$  and  $V=x^2y$  

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

A farmer wants to construct a rectangular pigpen using 400 ft of fencing. The pen will be built next to an existing stone wall, so only three sides of fencing need to be constructed to enclose the pen. What dimensions should the farmer use to construct the pen with the largest possible area?

• 100ft x 200ft

• 102ft x 196 ft

• 50 ft x 300 ft

• 50 ft x 175 ft

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

If y=2x-8, what is the minimum value of the product xy?

• -16
• -8
• -4
• 2

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.B.3